Q. 65.0( 2 Votes )

Using integration, find the area of the region bounded by the lines 2y=5x+7, the x-axis and the lines 2y=5x+7, the x-axis, and the lines x=2 and x=8.

Answer :

Given the boundaries of the area to be found are,


• The line equation is 2y = 5x + 7


• The y= 0, x-axis


• x = 2 (a line parallel toy-axis)


• x = 8 (a line parallel toy-axis)



As per the given boundaries,


• The line 2y = 5x + 7.


• x=2 is parallel toy-axis at 2 units away from the y-axis.


• x=8 is parallel toy-axis at 8 units away from the y-axis.


• y = 0, the x-axis.


• The four boundaries of the region to be found are,


Point A, where the line 2y = 5x + 7 and x=2 meet.


Point B, where the line 2y = 5x + 7and x=8 meet.


Point C, where the x-axis and x=8 meet i.e. C(8,0).


Point D, where the x-axis and x=2 meet i.e. D(2,0).


The line equation 2y = 5x + 7 can be written as,



Area of the required region = Area of ABCD.





[Using the formula and ]




The Area of the required region = 96 sq. units.


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